1. Option and Futures Markets
Chapter 4
Option and Futures Markets

2. A.Option Market Options
Call option: a contract that allows its holder to purchase a share of stock in the underlying company at a fixed price for a fixed length of time.

3. A.Option Market
Put option: a contract that allows its holder to sell a share of stock in the underlying company at a fixed price for a fixed length of time.

4. A.Option Market
1) Equity as a call option
B=S+P-C

5. A.Option Market Discrete put-call parity formula
Continuous compound put-call parity

6. B.Option pricing model (OPM) Black & Scholes (1973)
Binomial model
Assumptions
Stock price follows a binomial generating process
u: upward multiplier, u>0 no bound
d: downward multiplier, 0≦d<1
Perfect market q Su S Sd
1-q

7. B.Option pricing model (OPM)
Hedge ratio in risk-free hedge portfolios
In risk-free portfolio, Su-mCu=Sd-mCd
Hedge ratio m, q
Cu=max[0, Su-X] C
Cd=max[0, Sd-X]
1-q q
Su-mCu
S-mC
Sd-mCd
1-q

8. B.Option pricing model (OPM)
Call premium
Hedge
Prob. p
1- p

9. B.Option pricing model (OPM)
B-S Option pricing model
Assumption
Perfect market
Continuous trading opportunity
Stock returns follow a Geometric Brownian Motion Process.
Wiener process
Instantaneous Expected rate of return
Instantaneous S.D. of rate of return

10. B.Option pricing model (OPM)
Hedge ratio in risk-free hedge portfolio

11. B.Option pricing model (OPM)

12. B.Option pricing model (OPM)
Implications

13. C.Futures Market Futures Futures:
A contract that its holder was required to deliver or to buy a specified assets at a specified term on a specified expired date.
Types:Long, Short.
Commodities Futures: Corn, metal, etc.
Currency Futures:￡,￥, etc.
Financial Futures: T.B., T bond, etc.
Index Futures: S&P 500, etc.
Date: Contract date
Price, Specification, quality: standardized

14. C.Futures Market Futures market:
Participants: Floor Brokers, independents (CBOT)
Rules:
Marked to market

15. C.Futures Market Price limit: Minimum price fluctuation limit
Maximum daily price fluctuation
Clearing: Clearing house
Margin: Initial margin(3-15%)
Maintenance margin(75-80% of Initial Margin)
Open interest
Taxes: Hedgers, speculators

16. D.Commodity futures pricing
Storage theory
Normal Backwardation: Keynes& Hicks(1924)
Compound current spot rate
Storage cost
Convenience yield

17. D.Commodity futures pricing
Contango: Hardy(1923)
Unbiased expectation: Hartzmark (1987)

18. D.Commodity futures pricing
2. Financial futures pricing
Equilibrium,
Disequilibrium,

19. D.Commodity futures pricing
3. Synthetic Future Long